# Exercices for STK 4080 autumn 2012

Below are given exercises for the coming weeks and an overview of exercises that have been given to earlier weeks.

#### Exercises to coming weeks

*Week 48 (30 November), which is the last week with exercises:*

- Exam STK 4080 fall 2008 : Problems 3 and 4 (solutions ).

- Exam STK 4080 fall 2010 : Problems 1, 2 and 3 (solutions ).

#### Exercises to earlier weeks

*Week 47:*

- Additional exercise 3
- Practical exercise 12
- Exam STK 4080 fall 2008 : Problems 1 and 2.

Solutions to additional exercise 3 and the exam problems are given here

*Week 46:* Practical exercise 11 .

*Week 45:* Exercises 5.1 and 5.4 (solutions ) and practical exercise 10 . Note the corrections to exercise 5.1 given at the list of corrections .

*Week 44:* Exercises 4.3, 4.4, and 4.5 (solutions ) and practical exercise 9 .

*Week 43:* Additional exercise 2 (solution ) and practical exercise 8 .

In addition the students should work on the trial project . The students should make an extra effort to do the trial project, and those who are interested may hand it in for correction. The deadline is Monday 29 October. Comments on the solution of the trial project will be given in week 44.

*Week 42:* Exercises 4.1 and 4.2 (solutions to 3.12, 4.1, and 4.1 ). Practical exercise 7 . Note the correction to exercise 4.1 given at the list of corrections .

*Week 41:* Exercises 3.9, 3.10, 3.11, and 3.12 (solutions to 3.10 and 3.11 ). Practical exercise 6 .

Exercise 3.12 gives a nice illustration on the use of a number of the theoretical results on counting processes and martingales. The students should make an extra effort to do this exercise, and those who are interested may hand it in for correction. A solution to the exercise will be given in week 42.

Exercise 3.9 should be done using R. In practical exercise 4 it is described how you may read the data for exercise 3.9 into R.

*Week 40:* Additional exercise 1 (solution ; errors on pages 3 and 7 have been corrected 8 October), exercise 3.13, and practical exercise 5 . Exercise 3.13 should be done using R. The IUD data used in exercise 3.13 are described under Computing and they may be read into R by the command:

iud=read.table("http://www.uio.no/studier/emner/matnat/math/STK4080/h12/iud.txt",header=T)

For hints on R commands to exercise 3.13, see the R code to the lectures for week 39.

*Week 39:* Exercises 3.4, 3.5, 3.6, 3.7, and 3.8 (solutions ; errors on pages 6 and 7 have been corrected 8 October ). Practical exercise 3 and Practical exercise 4 . Exercises 3.4 and 3.7 should be done using R. In Practical exercise 4 it is described how you may read the data for exercises 3.4 and 3.7 into R. R code for exercises 3.4 and 3.7 and practical exercises 3 and 4 is given under Computing .

*Week 38:* Exercises 1.8, 1.10, 2.12, 3.1, and 3.3 (solutions ). Practical exercise 1 and Practical exercise 2 . R code for exercise 3.1 and practical exercises 1 and 2 is given under Computing .

*Week 37:* Exercises 2.5, 2.8, 2.10, and 2.11 (solutions ). After you have done exercises 2.5 and 2.8 you should read the material on covariance processes for time-continuous martingales and stochastic integrals on page 50 and the four last lines on page 51.

*Week 36:* Exercises 1.6, 1.9, 2.2, 2.4, 2.6, and 2.7 (solutions ).

*Week 35:* Exercises 1.1, 1.2, 1.3, 1.4, and 1.5 (solutions ).

*Week 34:* There were no exercises for this week.